Related papers: Configuration spaces as commutative monoids
We summarize our geometric and topological description of compact eight-manifolds which arise as internal spaces in ${\cal N}=1$ flux compactifications of M-theory down to $\mathrm{AdS}_3$, under the assumption that the internal part of the…
We investigate the enumerative geometry of point configurations in projective space. We define "projective configuration counts": these enumerate configurations of points in projective space such that certain specified subsets are in fixed…
Consider the configuration spaces of manifolds. We give a precise formula for the integral cohomological dimension (the degree of top non-trivial integral cohomology group) of unordered configuration spaces of manifolds with non-trivial…
Replacing configurations of points by configurations of tubular neighbourhoods (or discs) in a manifold, we are able to define a natural scanning map that is equivariant under the action of the diffeomorphism group of the manifold. We also…
While compactness is an essential assumption for many results in dynamical systems theory, for many applications the state space is only locally compact. Here we provide a general theory for compactifying such systems, i.e. embedding them…
We construct a configuration space model for a particular 2-colored differential graded operad encoding the structure of two $A_\infty$ algebras with two $A_\infty$ morphisms and a homotopy between the morphisms. The cohomology of this…
Consider the unordered configuration spaces of manifolds. Knudsen, Miller and Tosteson proved that the extremal homology groups of configuration spaces of manifold are eventually quasi polynomials. In this paper, we give the precise degree…
We study stability patterns in the high dimensional rational homology of unordered configuration spaces of manifolds. Our results follow from a general approach to stability phenomena in the homology of Lie algebras, which may be of…
We introduce and study smooth compactifications of the moduli space of n labeled points with weights in projective space, which have normal crossings boundary and are defined as GIT quotients of the weighted Fulton-MacPherson…
We prove the validity over $\mathbb{R}$ of a commutative differential graded algebra model of configuration spaces for simply connected closed smooth manifolds, answering a conjecture of Lambrechts--Stanley. We get as a result that the real…
Unimodularity is localized to a complete stationary type, and its properties are analysed. Some variants of unimodularity for definable and type-definable sets are introduced, and the relationship between these different notions is studied.…
In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology…
A generalized-homology bordism-theory is constructed, such that for certain manifold homotopy stratified sets (MHSS; Quinn-spaces) homeomorphism-invariant geometric fundamental-classes exist. The construction combines three ideas: Firstly,…
We study the rational homotopy types of classifying spaces of automorphism groups of smooth simply connected manifolds of dimension at least five. We give dg Lie algebra models for the homotopy automorphisms and the block diffeomorphisms of…
Bredon has constructed a 2-dimensional compact cohomology manifold which is not homologically locally connected, with respect to the singular homology. In the present paper we construct infinitely many such examples (which are in addition…
We study rank $1$ flat bundles over solvmanifolds whose cohomologies are non-trivial. By using Hodge theoretical properties for all topologically trivial rank $1$ flat bundles, we represent the structure theorem of K\"ahler solvmanifolds as…
Given a graded $E_1$-module over an $E_2$-algebra in spaces, we construct an augmented semi-simplicial space up to higher coherent homotopy over it, called its canonical resolution, whose graded connectivity yields homological stability for…
The article is devoted to the question whether the orbit space of a compact linear group is a topological manifold and a homological manifold. In the paper, the case of a simple three-dimensional group is considered. An upper bound is…
Moduli spaces of compact stable $n$-pointed curves carry a hierarchy of cohomology classes of top dimension which generalize the Weil-Petersson volume forms and constitute a version of Mumford classes. We give various new formulas for the…
We study equivariant projective compactifications of reductive groups obtained by closing the image of a group in the space of operators of a projective representation. We describe the structure and the mutual position of their orbits under…